HINDERED molecular rotation in solids reduces the width of their observed nuclear magnetic resonance spectra, with a consequent decrease in the measured second moments1. By contrast, on general theoretical grounds it has been shown2 that the second moments of dipolar-broadened spectra should remain invariant and should not be reduced by such motion. In a recent explanation3 of this apparent discrepancy the nuclear magnetic interaction was divided into two parts, namely, a steady mean interaction and a fluctuating part. The steady mean interaction is less than the interaction in a static crystal devoid of hindered rotation and generates an observed spectrum narrower than that of the static crystal. The fluctuating part of the interaction generates side-spectra set at integral multiples of the frequency of molecular rotation on either side of the central narrowed spectrum. Since the molecules do not rotate uniformly, but are re-oriented with an irregular motion, these side-spectra are dispersed over a band of frequencies with an intensity too weak to be observed. It was shown, however3, that when these weak side-spectra are included the second moment does indeed remain invariant even though the second moment of the central portion, which is all that is observed experimentally, becomes smaller.
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ANDREW, E., BRADBURY, A. & EADES, R. Nuclear Magnetic Resonance Spectra from a Crystal rotated at High Speed. Nature 182, 1659 (1958). https://doi.org/10.1038/1821659a0
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